An Analysis of Affine Coordinates for Pairing Computation

Kristin Lauter; Peter L.  Montgomery; Michael Naehrig

Paper 2010/363

An Analysis of Affine Coordinates for Pairing Computation

Kristin Lauter, Peter L. Montgomery, and Michael Naehrig

Abstract

In this paper we analyze the use of affine coordinates for pairing computation. We observe that in many practical settings, for example when implementing optimal ate pairings in high security levels, affine coordinates are faster than using the best currently known formulas for projective coordinates. This observation relies on two known techniques for speeding up field inversions which we analyze in the context of pairing computation. We give detailed performance numbers for a pairing implementation based on these ideas, including timings for base field and extension field arithmetic with relative ratios for inversion-to-multiplication costs, timings for pairings in both affine and projective coordinates, and average timings for multiple pairings and products of pairings.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Published elsewhere. Pairing 2010
Keywords: Pairing computation Miller's algorithm affine coordinates optimal ate pairing finite field inversions pairing cost multiple pairings pairing products.
Contact author(s): mnaehrig @ microsoft com
History: 2010-10-12: last of 2 revisions; 2010-06-25: received; See all versions
Short URL: https://ia.cr/2010/363
License: CC BY

BibTeX

@misc{cryptoeprint:2010/363,
      author = {Kristin Lauter and Peter L.  Montgomery and Michael Naehrig},
      title = {An Analysis of Affine Coordinates for Pairing Computation},
      howpublished = {Cryptology {ePrint} Archive, Paper 2010/363},
      year = {2010},
      url = {https://eprint.iacr.org/2010/363}
}